Author(s)

Yu Zhengping, Xu Yunqing

Corresponding Author

Xu Yunqing

ABSTRACT

In this paper, we give a method for generating cryptographically strong 44-bit S-boxes with the pure non-linear representatives of 3-quasigroup of order 4. S-boxes are widely used in block ciphers and hash functions and they are usually the only non-linear part in the systems and they have to be chosen carefully. 44-bit S-boxes are very suitable in the design of lightweight cryptographies, while the constructing of 44-bit S-boxes are usually by exhaustive computer search of permutations of degree 16. Our methodology is based on 3-quasigroup operations and it enables someone to get S-boxes optimal in linearity and differential uniformity, and all the component functions (algebraic normal form) of the generated S-boxes have maximal algebraic degrees.

KEYWORDS

S-Box, 3-Quasigroup, Latin Cube, Algebraic Normal Form